Believe it or not this comes from all the talk about theistic and atheistic faith issues that have come up lately.
Here is the premises:
If you flip a infinite number of coins a infinite number of times you will get a infinite number of coins that will never come up heads.
-but-
If you flip any one coin a infinite number of times it will hit heads and tails equally.
These 2 can’t coexist.
There is a saying that if you take a room full of monkeys and give them a typewriter and a infinite amount of time you will eventually get a copy of Hamlet. No we all know this could never happen either as monkeys will destroy the paper at a much higher probability then completing a single letter (barring evolution).
There seems like there is some limit on probability, when the chance of something happening is so so so small it is not just effectively zero it is zero and some things just can never happen*.
Now this is where the concept of God comes in, things like creation and life may have zero chance of happening on there own without a ‘God’.
(Not that I’m hanging my theists hat on this, as I don’t think God designed the system for Him to be proven, but I would like to see the responses.)
If statement A is correct then statement B is incorrect. The coin flipped in statement B could be one of the infinite amount of coins that will never come up heads. So there is no problem with both of these statements coexisitng. We just have a hard time wrapping our heads around how big a number infinite is
A coin can be fair (that is, have an equal intrinsic probability of turning up heads or tails on each successive flip) and still land tails-up on each individual flip for any finite* number of coin flips. There’s no contradiction here; the odds of it happening get infinitesimally small as the sequence of flips gets long, but the occurrence of a heads never becomes impossible (assuming a fair coin). It also never becomes certain. If it’s a fair coin, it’s even odds each flip, no matter what’s happened before.
Now, as I flip a coin and each time it comes up tails, I will gradually begin to doubt that it’s a fair coin, since it doesn’t seem to be behaving the way I’d expect a fair coin to act. But no amount of flipping will prove that a heads is impossible, and no number of flips is enough to guarantee that a heads will show. That’s not the nature of coin flips.
So out of curiousity, how does this relate to theology?
It is of course impossible to to flip a coin an infinite number of times. Don’t toy with him, Mikemike2.
What you’re addressing here is the basic unanswered question of cosmology: “Why is there something rather than nothing?” But invoking God does not answer that question. If God exists, God is something. Why does God exist rather than not existing? (And please don’t waste our time with the ontological argument! It’s bullshit!)
The contention that certain things like creation & life are too small probabilistically to happen on their own (with out a ‘designer’), they fall below a quantized threshold that makes things with such a small chance of happening actually zero chance of happening.
Oh, I get it. The answer is that “really improbable” does not mean “impossible”, no matter how improbable it is.
Plus, well, really improbable things become more probable with the amount of tries you have at them (assuming all you’re fighting against is probability). Given how many suns and maybe planets there are, and how long the universe has been around, hasn’t there been enough chances even for some really improbable things to occur, even if only once or twice?
(Plus maybe we’re not the only universe ever to happen. We dunno.)
Except there’s no evidence of that. Scientists who try cooking up life’s precursors in simulations of Earth’s early environment find it quite easy. From what I’ve read such arguments usually try to talk about a large, complicated DNA molecule or even a cell coming together by pure chance; not some simple molecules becoming self replicating, and only after much evolution becoming life. Also, they often ignore evolution’s abilty to weed out alternates, and ignore the natural tendancy of atoms and molecules to order themselves in various ways - something life exploits a LOT.
I did say “if”. I believe in the law of large numbers, but as long as were are dealing with the term infinite, there can be no answers as there is no point at which to measure.
You’ll never have an infinite number of coins, nor will you be able to flip a coin an infinite number of times, so these paradoxes are irrelevant for the real world.
To expect a run of n heads you’ll need 2^n coins. Flipping 1024 coins ten times each will get you one run of heads. Or rather, if you have a large number of trials flipping 1024 coins ten times each you’ll average one all-head run per trial. No matter how large your all-head run needs to be, there is a much larger number of coins which will make your all-head run probable.
In order to determine the likelihood of an improbable event we need a clear understanding of just how improbable it is. We don’t know that with life, but given the age and size of the universe, I’d bet the probability of life is pretty high. (We do know it isn’t zero, at least.)
Actually the theistic angle on the OP does assume it’s naturally impossible -thus making God (or something like it) necessary. If it’s merely unlikely, God is unnecessary.
Yes, and the universe is finite and had a limited amount of time available to develop life - so there is less chance of a complex thing happening if there is finite space and time then infinite space and time.
Yes, and the universe is finite and had a limited amount of time available to develop life - so there is less chance of a complex thing happening if there is finite space and time then infinite space and time.
If it can be proven that life (not to mention ‘creation’ itself) is impossible given infinite time and space, I would contend that it is also impossible with finite time and space
Remember also that the physical universe as we understand it was never “trying” to produce any particular form of life, much less the one that happened to evolve.
It’s like picking up a bridge hand of 13 cards dealt randomly from a pack of 52. For any particular hand, the odds of being dealt exactly that hand at random are about 1 in 400000000000000000000. (Yes, 20 zeroes. :eek: )
That’s orders of magnitude bigger than the number of seconds in the lifetime of the universe. Which means that if you were dealing one bridge hand per second from the birth of the universe to the present moment, the odds would still be thousands to one against your ever getting that particular hand.
And yet, that’s the hand that was dealt. Does this demonstrate statistically that there must be an Intelligent Designer of bridge hands who voluntarily stepped in and gave you that particular hand, rather than random chance?
By no means. The thing is that if you’re dealing bridge hands at random, you’re going to deal out some configuration of 13 cards each time. Each random configuration is just as unlikely as any of the others.
Similarly, the current precise configuration of the physical universe, including this particular set of carbon-based life forms existing on this particular planet orbiting this particular star, is indeed massively improbable. But then, so are all the other possible random configurations of the physical universe.
It would indeed be unrealistically unlikely that the universe could have evolved into any one pre-selected configuration purely at random. But there was no pre-selection involved. The universe could have happened to produce some other other kind of self-aware life form on a different planet near a different star; and if it had (or has), those other life forms would/will probably be just as awed as we are at the mind-boggling odds-beating improbability of their very existence. That doesn’t mean that there is any statistical reason to think that anything but chance and physical laws were involved in the process.
I raised this issue in February in this thread about improbable configurations of matter in an infinite universe.
In order to make such an argument you need to determine the probability of either event occurring spontaineously. Just saying “well gosh it SEEMS really, really unlikely” doesn’t cut it.
This is correct, I just realized my initial premise A was in error, the number of coins left converges on zero much faster then the number of flips approaching infinity, so yes you won’t have a single coin that fits that.
I believe in the law of large numbers, but as long as were are dealing with the term infinite, there can be no answers as there is no point at which to measure.